Abstract
The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite-dimensional superspaces, and construct super-analogs of the classical function spaces with a reproducing kernel — including the Bargmann–Fock representation — and of the Wiener–Segal representation. The latter representation requires the investigation of Wick ordering on Z2-graded algebras. As application we derive a Mehler formula for the Ornstein–Uhlenbeck semigroup on the Fock space.
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